2(2x-7)(2x+3)=0

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Solution for 2(2x-7)(2x+3)=0 equation: 


Simplifying
2(2x + -7)(2x + 3) = 0

Reorder the terms:
2(-7 + 2x)(2x + 3) = 0

Reorder the terms:
2(-7 + 2x)(3 + 2x) = 0

Multiply (-7 + 2x) * (3 + 2x)
2(-7(3 + 2x) + 2x * (3 + 2x)) = 0
2((3 * -7 + 2x * -7) + 2x * (3 + 2x)) = 0
2((-21 + -14x) + 2x * (3 + 2x)) = 0
2(-21 + -14x + (3 * 2x + 2x * 2x)) = 0
2(-21 + -14x + (6x + 4x2)) = 0

Combine like terms: -14x + 6x = -8x
2(-21 + -8x + 4x2) = 0
(-21 * 2 + -8x * 2 + 4x2 * 2) = 0
(-42 + -16x + 8x2) = 0

Solving
-42 + -16x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -8x + 4x2) = 0

Factor a trinomial.
2((-3 + -2x)(7 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1.5, 3.5}

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